Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction, and Random Matching

Incomplete information, local interaction, and random matching games all share a common structure. A type or player interacts with various subsets of the set of all types/players. A type/player's total payoff is additive in the payoffs from these various interactions. This paper describes a general class of interaction games and shows how each of these three classes of games can be understood as special cases. Techniques and results from the incomplete information literature are translated into this more general framework; as a by-product, it is possible to give a complete characterization of equilibria robust to incomplete information (in the sense of Kajii and Morris [1995]) in many-player binary action coordination games. Only equilibria that are robust in this sense [1] can spread contagiously and [2] are uninvadable under best response dynamics in a local interaction system. A companion paper, Morris [1997], uses these techniques to characterize features of local interaction systems that allow contagion.